Question

The production function at Jerry’s Copy Shop is q=1000min(L,3K)
, where *q* is the number of copies per hour, *L* is
the number of workers, and *K* is the number of copy
machines. Draw the following graphs. The graphs should have the
number of workers, *L*, on the x-axis.

Draw the isoquants for this production function for *q* =
1000, 2000, and 3000. [4 pts.]

Draw the total product of labor (TP_{L}), average
product of labor (AP_{L}), and marginal product of labor
(MP_{L}) curves for this production function, assuming K =
1. [6 pts.]

Answer #1

a) Isoquants are drawn below. For q = 1000, we have 1000 = 1000min(L, 3K) implying min(L, 3K) = 1 for L = 3K, = 1

For q = 2000, we have 2000 = 1000min(L, 3K) implying min(L, 3K) = 2 for L = 3K = 2.

For q = 3000, we have 3000 = 1000min(L, 3K) implying min(L, 3K) = 3 for L = 3K = 3

b) The graph is provided below. For L = 0, 1 and 2, we see that output is q = 1000min(0, 3) or 0, q = 1000min(1, 3) = 1000 or q = 1000min(2, 3) = 2000. For L = 3, 4, and so on, q is fixed at 3000. APL = TPL/L and MPL is the difference of TPL for two labor units.

Labor | Output/TPL | MPL | APL |

0 | 0 | ||

1 | 1000 | 1000 | 1000 |

2 | 2000 | 1000 | 1000 |

3 | 3000 | 1000 | 1000 |

4 | 3000 | 0 | 750 |

5 | 3000 | 0 | 600 |

6 | 3000 | 0 | 500 |

7 | 3000 | 0 | 428.6 |

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